Motion of Pendulum Interrupted by a Peg

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This Demonstration shows the movement of a simple pendulum whose swing is interrupted by a peg.

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The pendulum is a bob of arbitrary mass connected to a pivot at by a perfectly flexible, massless string of length 1. A peg is located directly below the pivot at a distance . The initial angle between the string and the vertical is .

To keep the string taut and prevent the bob from falling down, we have as limiting conditions for the height of the interrupting peg: and for the initial angle: .

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Contributed by: Erik Mahieu (December 2011)
Open content licensed under CC BY-NC-SA


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Details

Each complete period is a sequence of four quarter-periods: two for a pendulum of length 1 and initial angle when the bob is to the right of the vertical and two for a pendulum of length and initial angle when the bob is to the left. The quarter-periods are determined by solving the appropriate ODE and escaping the solution using Mathematica's built-in "EventLocator" method.

An interesting article on the subject is C. E. Mungan. "Maximum Bob Height of an Interrupted Pendulum." United States Naval Academy Physics Department. (2006) usna.edu/Users/physics/mungan/_files/documents/Scholarship/InterruptedPendulum.pdf.

See also the Demonstration by Enrique Zeleney, "Interrupted Pendulum".



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